Long-distance communication can enable collective migration in a dynamic seascape

Social information is predicted to enhance the quality of animals’ migratory decisions in dynamic ecosystems, but the relative benefits of social information in the long-range movements of marine megafauna are unknown. In particular, whether and how migrants use nonlocal information gained through social communication at the large spatial scale of oceanic ecosystems remains unclear. Here we test hypotheses about the cues underlying timing of blue whales’ breeding migration in the Northeast Pacific via individual-based models parameterized by empirical behavioral data. Comparing emergent patterns from individual-based models to individual and population-level empirical metrics of migration timing, we find that individual whales likely rely on both personal and social sources of information about forage availability in deciding when to depart from their vast and dynamic foraging habitat and initiate breeding migration. Empirical patterns of migratory phenology can only be reproduced by models in which individuals use long-distance social information about conspecifics’ behavioral state, which is known to be encoded in the patterning of their widely propagating songs. Further, social communication improves pre-migration seasonal foraging performance by over 60% relative to asocial movement mechanisms. Our results suggest that long-range communication enhances the perceptual ranges of migrating whales beyond that of any individual, resulting in increased foraging performance and more collective migration timing. These findings indicate the value of nonlocal social information in an oceanic migrant and suggest the importance of long-distance acoustic communication in the collective migration of wide-ranging marine megafauna.


Purpose
The purpose of this individual based model (IBM) is to investigate the role of foraging and long-range social information in driving the yearly southward breeding migration of Northeastern Pacific blue whales.

Entities, state variables, and scales
Entities or agents in the IBM represent a single whale.State-variables track how each agent moves through and experiences the domain.The domain spans 116-128 • W and 32-44 • N and is divided into 3 km × 3 km spatial patches.Each patch is assigned a sea surface temperature (SST; • C) and near surface krill abundance.
The SST and krill density are updated daily (24 hours) and are provided from an implementation of ROMS (see 1.6).
To investigate drivers of southward migration, we use a series of IBMs, each of which is designed with a distinct southward migration mechanism based on a combination of environmental and social information.
The IBMs are formulated as a state-switching model with four behavioral states representing transit and forage behaviors during the foraging season and breeding migration.In all models, each agent is assigned the following state-variables: behavioral state, location, SST, and krill (Table 1).In models with social calls the three additional state variables of sex, calling behavior, and received call signals are assigned.
One time step represents 6 hours (4 time steps/day) and simulations were run for 180 days.Each simulations includes 2,000 agents.Simulations are run for years 1990-2010.

Process overview and scheduling
The model progresses in 6 hour time steps.Within each time step, the state-variables for each agent are updated following the order displayed in Figure 1.Environmental state variables are updated every 24 hours Collectives: Agents do not belong to any collective unit.
Observation: During model simulations, the behavioral state, cumulative krill intake, average recent krill intake, calling behavior, and received calls are recorded for each agent on each time step.These quantities contribute to the selection of behavioral states and provide a useful comparison between distinct migration mechanisms.
Calling behavior only impacts the behavioral states and decisions of agents in the models with social behavior.However, in practice, calling behavior can be monitored in all models.

Initialization
Since we are interested in factors driving the breeding migration, models are initiated on July 1st.Agents' initial locations are selected uniformly at random within areas of climatologically high krill densities from the ROMS data Abrahms et al., 2019.Regions of climatologically high krill were defined by averaging the krill abundance on July 1st 1990-2010 for each spatial grid cell, then thresholding the averages.
At the start, 50% of agents are randomly assigned to be male, an important fact since the primary producer of long-distance song are males.

Input data
The environmental variables SST and near-surface krill abundance are precomputed and supplied as input data to the IBM.These variables are precomputed using a Regional Ocean Modeling System (ROMS) implementation that is specifically parameterized for the California Current region (Fiechter et al. 2018;Fiechter et al. 2020).Additionally, the ROMS implementation has been coupled with NEMUCSC, a biogeochemical model adapted from the North Pacific Ecosystem Model for Understanding Regional Oceanography of Kishi et al. (2007), and provides the krill concentrations.ROMS-NEMUCSC data that spans the domain is available for the years 1990-2010 at 3km spatial resolution and daily temporal resolution.Simulated krill concentrations have been evaluated against existing in situ data for May-June and are expected to adequately reproduce observed krill aggregation regions during the upwelling season (Fiechter et al., 2020).This data is available at https://doi.org/10.7291/D1KD4J.

Submodels and Model Details
This section represents the Submodels portion of the ODD protocol.Subsections define the processes in Figure 1.
Throughout the model description, the subscript n will indicate a quantity or variable for an individual agent, where n ∈ {1, 2, . . ., 2000}.Additionally, t is used to represent the time step of the simulation.Model time steps are 6-hours in length and simulations are initiated on July 1 (t 0 ).The yearday t can be extracted from the time step t using the floor-function as t = t 0 + ⌊ t 4 ⌋.Variables are summarized in Table 2 and all notation and variable names are consistent with that of the main text.Additionally, variables with an overbar (for example, xn ) are consistently defined to be averages in time.

Social Communication
The social communication process is divided into the call producers and call receivers.

Call Producers
The call signal sent by agent n on at time step t is defined as where xn (t) denotes the average 24-hour foraging behavior Here, xn (t) takes on a value between 0 and 1, with 0 representing all transit and 1 all forage behaviors.
The call signal δ n (t) is intended to be a time-dependent measure of foraging success analogous to the ratio CI night :CI day (Oestreich et al., 2022;Oestreich et al., 2020).
At the start of the simulation, 50% of agents are randomly assigned as male (call producers) and on each time step, a subset of male whales are randomly selected to produce calls.The proportion of male whales calling on each time step increases linearly from 5% on July 1 to 30% on December 31.

Call Receivers
Define M n (t) to be the subset of whales whose calls are heard by whale n at t, N n (t) = |M n (t)| (cardinality of the set M n (t)) to be the number of calls received, and R j,n (t) the distance (in meters) between two agents n and j.Then, the call signal received by whale n at time t, σ n (t), is an average of all calls received on that timestep, weighted by the inverse-square law dependent decay of the call amplitude Call

Selecting behavioral states
The four behavioral states S 1,2,3,4 represent transiting and foraging behaviors during the northward foraging and southward breeding migrations.Each behavioral state is associated with characteristic movements defined by step length and turning angle distributions.
Transitions between the four behavioral states S 1,2,3,4 are governed by the state transition probability matrix τ defined by where s n (t) ∈ {1, 2, 3, 4} is the behavioral state of whale n at time step t.Allowed transitions are show in the schematic in Figure 1 in the main text.
Southward migration strategies are incorporated in the southward transition probability p * .Tested migration strategies are based on a combination of an agent's personal foraging behavior and received social information.
As defined in the main text, we set ωn (t) to be the average foraging effectiveness (average krill intake) and σn (t) to be the average received social information of agent n over a period of T = 40 timesteps (10 days).
These are defined by Migration strategies are encoded in the transition probability p * = P (s n (t + 1) = 3|s n (t) ∈ {1, 2}).The transition probability functions associated with each strategy are given below.Although the subscript n is omitted, all transition probabilities are assigned for each agent.All parameters are included in Table 3.
1. Individual foraging efficiency (personal): 2. Individual foraging efficiency and minimum krill intake (personal & min krill): 4. Individual foraging efficiency and social communication (personal & social): The personal, social, and personal & social strategies and their results are described in detail in the main text.In the Supplementary Results (Section 8), we additionally include results of a migration strategy with a minimum krill intake requirement which acts as a proxy for an energetically-driven migration strategy.
Specifically, agents are only able to migrate if their krill intake exceeds a minimum krill threshold κ min .
Thus, define the function where the cumulative krill intake κ n (t) is found by summing the krill density ρ at the agent's foraging locations State transition probabilities are computed as follows.First, p * is computed and fixed.Then, for agents in S 1,2 the probabilities p 1 and p 2 are defined using the fact that the rows of the STPM sum to 1. Thus, the probabilities are set to where P E,K (s n (t + 1) = 2|s n (t) ∈ {1, 2}; SST, ρ) is the probability of foraging due to SST and krill density defined in (Dodson et al., 2020).Parameter values for the forage-transit selection process are identical to those in (Dodson et al., 2020).Transition probability functions between S 1 and S 2 are identical across all presented models.
For agents in S 3,4 , we likewise define the probability of foraging and utilize that p 3 + p 4 = 1.Thus, where p 4 has a stricter foraging threshold (high krill density required for foraging).Transition probabilities between S 3 and S 4 are identical across all presented models that include the southward behavioral states.

Sampling Environmental Conditions and Movement Updates
On each time step, agents sample and store as state variables the SST and krill density at their current location (values from simulated ROMS-NEMUCSC data).These environmental parameters are used to compute the elements of the state transition probability matrix.
Regardless of migration strategy, movement updates are selected from distinct turning angle and step length distributions associated with characteristic transit and forage behaviors.That is, movement updates depend on the selected behavioral state.These movement distributions were parameterized from empirical data (Bailey et al., 2009) and are additionally defined in previous model iterations (Dodson et al., 2020).We point to these sources for further details.
Turning angles for states S 1,2,4 are defined as a deviation from the current trajectory of an individual, with a 0 • turning angle corresponding to an agent continuing straight along its path connecting the locations at the current and previous time steps.For agents in state S 3 , a 0 • turning angle corresponds to southward migration with the agent heading towards latitude 32 • N and longitude 119 • W; this point was chosen to replicate a southward migration trajectory consistent with heading toward the southern breeding grounds.

Model Assumptions
Here, we summarize and clarify model assumptions.
• Behavioral states and positions are updated every six hours.Transition probabilities within the north and southward migration categories (between states S 1 → S 2 and S 3 → S 4 ) are based only on SST and prey levels.
• Transition probabilities between S 1 → S 2 are identical across all presented models.
• Transition probabilities between S 3 → S 4 are identical across all presented models that include the southward behavioral states.
• Individuals commit to southward migration and are not permitted to transition from states S 3,4 to S 1,2 .
• Agents are not bound to the domain and will freely leave if their movement updates take them outside the domain.
• Since we are interested in factors driving the breeding migration, the model is initiated on July 1st.
Agents' initial locations are selected uniformly at random within areas of climatologically high krill densities from the ROMS data (Abrahms et al., 2019).
• Tested migration mechanisms represent strategies based only on foraging history, information gathered from social calls, and year-day (null model).

Null Models
Model results are tested against two null models.The first null model, a hypothetical non-migratory population, is described in the main text and is the two-state model of Dodson et al., 2020.The second null model follows a yearday-driven migration strategy.Migration dates for individuals in the yearday model are pre-determined and follow a normal distribution with a mean of 310 (November 6) and standard deviation of 20 days.The mean and standard deviation represent average historical trends in blue whale migrations and average call behavior recorded from the MARS hydrophone (Oestreich et al., 2022;Oestreich et al., 2020).
The yearday-driven null model provides a extrinsically-based modeled population for comparison.
Comparison of migration dates from Monterey Bay hydrophone data and modeled migration mechanisms.Model data aggregated across all 21 years.Migration statistics for each modeled migration mechanism were calculated using the subset of the agents whose migration initiated north of Monterey Bay (specifically north of 36 • N).Boxplots show the distribution of year median migration dates (shown in gray dots).The boxplot labeled hydrophone is empirical data from the Montery Bay hydrophoneOestreich et al., 2020.The (*) label indicates a statistically significant difference between the set of median migration dates of the modeled mechanism and the hydrophone dataset and the (NS) label indicates no significant difference.Whitney U-test (p-values in Table4) indicates that both the set of median migration dates for the personal and personal & minimum krill strategies are statistically different from the set of hydrophone median migration dates.The migrations of the socially informed populations and null day of year are not statistically significantly different from the hydrophone data.However, the spread of the null yearday population is much narrower than the empirical hyrdophone data.Second, the median migration dates of the full simulated populations (not just the individuals whose migration initiated north of Monterey Bay) are compared to each other and the median date of blue whales departing the U.S. Exclusive Economic Zone (EEZ) found from empirical tagging studies inIrvine et al., 2014.The EEZ departure dates from Irvine et al., 2014 include a large range of whale locations and latitudes, hence it is appropriate to compare this set of empirical data with the full simulated population.

Figure 6
Figure6shows the median migration dates of the full population of all strategies compared with the median EEZ departure date.The dashed purple line shows October 21, the median date of blue whales departing the U.S. Exclusive Economic Zone (EEZ) found from empirical tagging studies inIrvine et al., 2014.On average, the migration dates of the full population are lower than the subset whose migration initiated from northern latitudes.Additionally, migration dates of the social migration strategies are found to be compatible with signals are capped at a maximum radius R max .Calling behaviors and the inverse-square law amplitude decay are independent of call radii.Calling and migration model parameters.Summary and descriptions of model parameters related to calling behavior and southward migration.Model results computed using default parameter values.Sensitivity analysis conducted over the listed range of values.Parameter values with no listed range were not included as part of the sensitivity analysis.Parameters without units are unitless.
n (t) Krill density at location of whale n at time step t xn (t) Daily foraging rate of whale n at time step t δ n (t) Call signal sent by whale n at time step t σ n (t) Call signal received by whale n at time step t σn (t) Average call signal received by whale n over the past T time steps ωn (t) Foraging effectiveness of whale n at time step t (averaged over previous T time steps) τ State transition probability matrix Supplementary Table S 2: Model variables.Summary and descriptions of model variables.